The invention relates to a method and apparatus for the multiplication of electrical signals. The invention is particularly useful in the analysis of vibrations and in balancing techniques. However, the invention is not limited to this field but may be used wherever signals must be multiplied.
Several methods are known in the art for multiplying electrical signals. Examples of such methods are the so-called transconductance multiplication, the Hall multiplication, the resistance modulation, the parabola (square law) multiplication, multiplication by means of a D/A converter, and the like. These methods multiply signals which are of the same or different types, such as voltages, currents, flux densities, and other signals. These known methods are based on different principles and are used for various purposes.
Multiplication of electrical signals is often employed when analyzing oscillations and when determining the unbalance of a rotating body. In each instant a single frequency component is determined from a mixture of oscillations. The oscillation mixture is present as an electrical measurement signal. The frequency component is ascertained by multiplying the measured signal such as a voltage by a sinusoidal reference oscillation. The amplitude or value of the frequency component of interest is obtained very accurately by averaging the output signal of the multiplier.
A disadvantage of the previously known methods is that an error accompanies the electrical or electronic methods which generate the product of the signals. Such an error is inherent in the product formation of the signals to be multiplied. In describing an electronic multiplier one starts with two input values X(t) and Y(t) and an output value A(t). For an ideal electronic multiplier, the following is true: EQU A(t) = X(t) .multidot. Y(t)
However, errors accompany the execution or technological realization of such a multiplier. The errors involved are particularly the zero point errors X.sub.os and Y.sub.os of the two inputs X and Y, respectively, the zero point error A.sub.os of the output A, as well as the errors caused by nonlinearities of the multiplier. These errors are disturbingly conspicuous in the multiplication arrangements of the prior art.